Solve for $x$ and $y$ using elimination. ${-2x+2y = 18}$ ${6x+3y = 36}$
We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the top equation by $3$ ${-6x+6y = 54}$ $6x+3y = 36$ Add the top and bottom equations together. $9y = 90$ $\dfrac{9y}{{9}} = \dfrac{90}{{9}}$ ${y = 10}$ Now that you know ${y = 10}$ , plug it back into $\thinspace {-2x+2y = 18}\thinspace$ to find $x$ ${-2x + 2}{(10)}{= 18}$ $-2x+20 = 18$ $-2x+20{-20} = 18{-20}$ $-2x = -2$ $\dfrac{-2x}{{-2}} = \dfrac{-2}{{-2}}$ ${x = 1}$ You can also plug ${y = 10}$ into $\thinspace {6x+3y = 36}\thinspace$ and get the same answer for $x$ : ${6x + 3}{(10)}{= 36}$ ${x = 1}$